Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}-2x-8y &= 1 \\ 2x+4y &= -2\end{align*}$
Begin by moving the $y$ -term in the second equation to the right side of the equation. $2x = -4y-2$ Divide both sides by $2$ to isolate $x$ $x = {-2y - 1}$ Substitute this expression for $x$ in the first equation. $-2({-2y - 1}) - 8y = 1$ $4y + 2 - 8y = 1$ Simplify by combining terms, then solve for $y$ $-4y + 2 = 1$ $-4y = -1$ $y = \dfrac{1}{4}$ Substitute $\dfrac{1}{4}$ for $y$ in the top equation. $-2x-8( \dfrac{1}{4}) = 1$ $-2x-2 = 1$ $-2x = 3$ $x = -\dfrac{3}{2}$ The solution is $\enspace x = -\dfrac{3}{2}, \enspace y = \dfrac{1}{4}$.